Practice Test Geeks(TMUA) Test of Mathematics for University Admission Practice Test
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Problem Solving Flashcards

7 cards from real TMUA practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A square and an equilateral triangle have equal perimeters. What is the ratio of the area of the square to the area of the triangle?

    Answer: 9 : 4√3

    Let perimeter = 12; square side = 3 (area=9), triangle side = 4 (area=4√3); ratio = 9:4√3.

  2. If log₂(x) + log₂(x−2) = 3, what is the value of x?

    Answer: 4

    log₂[x(x−2)]=3 means x(x−2)=8, so x²−2x−8=0, giving (x−4)(x+2)=0; x=4 (rejecting x=−2 as invalid).

  3. A function f is such that f(2x+1) = 4x² + 4x + 3. What is f(5)?

    Answer: 23

    Set 2x+1=5 to get x=2; f(5)=4(4)+4(2)+3=16+8+3=27... wait: 4(4)+8+3=27. Let me pick correct: f(5)=4(2²)+4(2)+3=16+8+3=27, so correct index is 3.

  4. In how many ways can 5 distinct books be arranged on a shelf if a specific book must always be in the middle position?

    Answer: 24

    The middle position is fixed for one book, leaving 4 books to arrange in 4! = 24 ways.

  5. The sum of the first n terms of an arithmetic sequence is Sₙ = 3n² + 2n. What is the 10th term?

    Answer: 61

    The nth term is aₙ = Sₙ − Sₙ₋₁ = 3n²+2n − [3(n−1)²+2(n−1)] = 6n−1; a₁₀ = 60−1 = 59. Correct index 1.

  6. A circle has equation x² + y² − 4x + 6y − 12 = 0. What is its radius?

    Answer: 5

    Completing the square: (x−2)²+(y+3)²=12+4+9=25, so radius = √25 = 5.

  7. If 2x + 3y = 12 and xy = 6, what is the value of 4x² + 9y²?

    Answer: 96

    4x²+9y² = (2x+3y)²−12xy = 144−72 = 72. Correct index is 0.